You don't need a new form for each person. You need to send users an editing form. Auto-filling in this case is a form of updating an existing record. This basically means the form would be prefilled with the "submitter" name.

When you access the form directly you are only able to create new records (which is not what you want). Instead, you need to add the editing formula to your Airtable. It would generate a unique URL for each record and you can then share those URLs with your clients. That would allow them to click on a link to open their form and fill it.

Make sure to watch the instructional video here. It guides you step-by-step on how to set this up.